This is an announcement for the paper "The metric geometry of the Hamming cube and applications" by F. Baudier, D. Freeman, Th. Schlumprecht and A. Zsak.
Abstract: The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the $C(K)$-distortion of important classes of separable Banach spaces, where $K$ is a countable compact space in the family $ { [0,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot n],\dots,[0,\omega^\omega]}\ ,$ are obtained.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B85
Submitted from: schlump@math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.4376
or